AYP Vol. II: Archontic (Civil) Year Calendar Intercalations

APPENDIX III ARCHONTIC (CIVIL) YEAR INTERCALATIONS The Placement of Embolismic Months Chapter from the forthcoming Athenian Year Primer Vol. II. The excerpt presupposes familiarity with the methodologies and arguments presented in AYP. Chapter tackles one of the most fundamental and crucial yet least understood calendrical practices, which all lunisolar calendars must follow: insertion of an extra (thirteenth) lunar month to keep a lunar year’s Synodic Cycles aligned to a Sidereal Solar Year (i.e., solstice ↔ solstice or equinox ↔ equinox). 1) Show that ancient Greeks across the ancient Aegean proved far more astronomically savvy than currently appreciated. 2) Argue that ancient Athenians could not have used any fixed or absolute thus, in effect, arbitrarily inserted embolismic month to keep Archontic Years aligned. Significant, existential (practical) considerations existed. 3) Consequently, also argue that intercalations must have possessed “rules” or at least firmly established “guidelines.” The most obvious in fact being any number of seasonal festivals (e.g., Anthesteria, Eleusinian Mysteries). Seasonal festivals, moreover, promptly follow all Panhellenic gatherings (addressed in subsequent Chapters). 4) Attempt to unlock the methodologies used so one can not only understand the underlying math but also establish the base astronomical “template.” 5) Finally, knowing what Calendar Equations ought have occurred aids greatly when working with recovered epigraphical evidence that display such equations. When any deviations surface, we can develop a thorough understanding of why they took place. Copyright © 2023 by Christopher Planeaux. Published in the United States of America by Westphalia Press. Washington D.C.. Manufactured in the United States of America. First Edition, 2020. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing from the author. Within the United States of America and the United Kingdom, exceptions are allowed in respect of any fair dealing for the purpose of research or private study, or criticism or review, as permitted under United States Copyright Law. This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired-out, or otherwise circulated in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser without the author’s prior consent Text typeset in Bookman Old-style. Footnotes typeset in Palatino. Endnotes typeset in Palatino Linotype Ancient Greek text typeset LS Odyssea. Ancient Greek notes typeset LS Payne Condensed. Ancient Greek typesets available from Linguist’s Software, Inc. Cover Illustrations: Background: The Celestial Sphere National Aeronautics and Space Administraion Insert: IG I3 369 frag. k (=IG I2 324 frag. k) Superimposed with Plate I restoration from B. Meritt’s The Athenian Calendar ISBN: [Pending] CHAPTER XX J CIVIL CALENDAR INTERCALATION Note: this chapter supersedes AYP 159-160 and expands considerably upon the brief Intercalation schemas given pp. 177-180 and therefore also affects Appxs. IV-VI & X-XI. A functional lunisolar calendar requires constant and continuous observations of but two celestial objects: the Moon against the Sun. Ancient Athenian astronomers reckoned four key solar events against four of twelve (or thirteen) lunar events throughout a given “year.” This patent obviousness masks a underlying complexity: their combined movements will at times prove frustratingly ambiguous. Let us assume all ancient Greek povlei~ attempted, however imperfectly, to keep Civil Months aligned with the Moon and then Civil Years aligned to the Seasons. Calendrical deviations from the sky should not a priori indicate indifference or evidence the basileuv~ (or ejkklhsiva) wantonly inserted or omitted days (or whole months) but also entertain that some may have reflected observational uncertainties, which required human decisions. The Moon appears illumed possessing the same phase from every location on Earth, i.e., within the same hemisphere each side of the equatorial line (AYP 116-117). The most important astronomical quality to know for the arrival of a 1stVisCres becomes the Moon’s elongation (AYP 116, 239-243). The math remained unknown to ancient Greeks, but the varying sizes and elevations the initial, readily visible crescents possessed month to month could not have eluded even casual observations. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS Under optimal viewing conditions, the lunar crescent will first become observable on the same day (sans topographical obstructions) from Makedonia to Babylon to Egypt to Syracuse to Korkyra (and of course everywhere in between). In other words, ancient Athenians, Spartans, Thebans, Epidaurians, Eleans, Nemeans, Delians, Corinthians et al. would all gaze upon the same Moon on the same night every synodic cycle. 13 Consequently, the counts of synodic cycles between solar or stellar events, e.g., VerEqu to AS a CMa (Seirios) remained the same every year for all ancient Greek povlei~ regardless what time of year their Civil Years began (relative to each other). This astronomical certainty permitted fiercely independent ancient Greek povlei~, who zealously protected their aujtonomiva, ejleuqeriva, and aujtokravteia, to develop and maintain local, internally functional yet quite different lunisolar calendars that also progressed coterminous or at least parallel with each other. Despite the (apparently still) prevailing communis opinio that ancient Greek calendars developed and stood horrifically chaotic and haphazardly diverged from one another, the premise ultimately proves untenable. The posit collapses for one reason above all others: annual, biennial, quadrennial, quintennial et al. Panhellenic Festivals. Participants, in short, needed to know when to gather again at quite distant locales well in advance. The Basics The math, which determines when extra ancient Attic Civil Months needs inserted, proves surprisingly straightforward. If the current Civil Year’s 1stVisCres appeared < 21 days after SumSol, then the next Civil Year becomes embolismic. More precisely, the thirteenth synodic cycle after each SumSol runs (read L → R): Days SumSol to 1stVisCres Current Civil Year Next Civil Year Following Civil Year 10 ↔ 12 0↔1 -11 ↔ -10 13 ↔ 15 2↔4 -9 ↔ -7 16 ↔ 17 5↔6 -6 ↔ -5 18 ↔ 21 7 ↔ 10 -4 ↔ -2 During all Ordinary Attic Civil Years, moreover, four specific Civil Months naturally and always aligned to four specific Solar Events: Boid = AutEqu; Pos = WinSol; Elaph = VerEqu; and Skir = SumSol. The premise: embolismic years sought to preserve these alignments. Nothing more complicated than math proves necessary but comes with a question: whether a solstice or equinox ought always fall during the nominal Civil Month or could have fallen during its embolismic partner. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS When composing the Primer, I did not give this question much thought. Regardless, as with everything regarding ancient Attic time-reckoning, “best practices” cannot become “inflexible rules.” Undoubtedly different basilei`~ facing different circumstances could choose (or recommend to the ejkklhsiva) different courses of actions down through the centuries. We shall return to this specific question end of chapter. For now, if an anchor solar event ought fall during the nominal Civil Month, then intercalations progress inside small count-ofday windows. When reckoning solstices and equinoxes by a Boö (AYP 157-160), the numbers of days between events ran (note: Julian-Gregorian Leap Year = 4): → → → → SumSol AutEqu WinSol VerEqu AutEqu WinSol VerEqu SumSol = = = = Yr 1 Yr 2 Yr 3 Yr 4 92 87 91 95 365 92 88 90 (91) 95 (94) 365 92 88 91 95 366 91 88 91 95 365 a Ancient Athenian astronomers then ran six systematic Civil Month scenarios to establish “baseline” noumhnivai for Civil Months IV, VII, X, and (the following) I: 1) FHFHFHFHFHFH & 2) HFHFHF HFHFHF; 3) FFHHFFHHFFHH & 4) HHFFHHFFHHFF; then 5) FF FHHHFFFHHH; and 6) HHHFFFHHHFFF. Scenario 1: 2: 3: 4: 5: 6: Days Days Days Days Days Days = = = = = = 1 Pyan 1 Gam 1 Moun 1 Hek 90 89 90 89 91 88 178 178 179 177 178 178 267 266 267 266 268 265 355 355 355 355 355 355 (89) (90) (90) (89) (88) (91) (90) (89) (89) (90) (91) (88) (89) (90) (90) (90) (88) (91) These six scenarios represent ideal count averages (essentially) from one extreme to the other. Pyan noumhniva could fall Day 8891; Gam noumhniva Day 177-179; Moun noumhniva Day 265-268; with Hek noumhniva always on Day 355. During the years covered by the Primer, however, a seventh plhvrh~ month occurred sixteen times: 460/59, 452/1, 451/0, 443/2, 441/0, 434/3, 432/1, 429/8, 424/3, 418/7, 415/4, 408/7, 405/4, 400/399, 399/8, and 396/5 BCE. These introduced ±1 solar day by end-of-year. a) Prior to Meton & Euktemon (463 – 432 BCE), ancient Athenians ought have reckoned SumSol 29, 29, 29, 30 Jun; AutEqu 29, 29, 29, 28 Sep; WinSol 25, 26, 26, 26 Dec; and VerEqu 26, 26, 27, 26 Mar; after 432 BCE , SumSol 28, 28 , 28, 29 Jun; AutEqu 28, 28, 28, 29 Sep; WinSol 24, 25, 25, 25 Dec; and VerEqu 25, 25, 26, 25 Mar. As a consequence, Yr 2 shifted to 92 88 91 94 (Chap. XX, pp. xxx-xxx). CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS The next required variable becomes the number of days after SumSol the initial 1stVisCres actually appeared. Working large to small for illustration purposes, deviations run: 461/0 BCE: SumSol = Day 1 29 Jun AutEqu = Day 92 → → 1 Hek = 1 Pyan = 28 Sep WinSol = Day 180 → = Day 271 → SumSol = Day 366 → Days 96 – 99 2 – 5 Oct 1 Gam = Days 185 – 187 1 Moun = Days 273 – 276 1 Hek = Day 362 25 Dec VerEqu Day 8 7 Jul 31 Dec – 2 Jan 26 Mar 28 – 31 Mar 29 Jun 26 Jun Next 1 Hek arrives four days before SumSol, but AutEqu would still fall in Boid, WinSol in Pos, and VerEqu in Elaph. The basileuv~ (or ejkklhsiva) could have inserted an embolismic Moun, Thar, or Skir without any (apparent) seasonal disruption. 439/8 BCE: SumSol = Day 1 29 Jun AutEqu = Day 93 → → 1 Hek = 1 Pyan = 29 Sep WinSol = Day 181 → = Day 272 → 1 Gam = 1 Moun = Day 367 → Days 183 – 185 28 – 30 Dec 27 Mar SumSol = Days 94 – 97 30 Sep – 3 Oct 26 Dec VerEqu Day 6 5 Jul Days 271 – 274 26 – 29 Mar 1 Hek = 30 Jun Day 361 24 Jun Next 1 Hek arrives five days before SumSol. AutEqu still falls in Boid and WinSol in Pos. VerEqu, on the other hand, possessed a 50% chance of falling in Moun. The basileuv~ (or ejkklhsiva) could have therefore inserted an embolismic Pos, Gam, Anth, or even Elaph. A seasonal disruption, however, might take place. 409/8 BCE: SumSol = Day 1 28 Jun AutEqu = Day 92 → → 1 Hek = 1 Pyan = 28 Sep WinSol = Day 179 → = Day 271 → 1 Gam = Day 366 → 28 Jun Days 181 – 183 25 – 27 Dec 1 Moun = 26 Mar SumSol = Days 92 – 95 27 - 30 Sep 24 Dec VerEqu Day 4 2 Jul Days 269 – 272 23 – 26 Mar 1 Hek = Day 359 22 Jun This alignment proves trickier. Next 1 Hek arrives six days before SumSol. AutEqu, however, had but a 75% chance of falling CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS in Boid. WinSol falls squarely in Pos, but VerEqu then possessed a 50% chance of falling in Moun. The basileuv~ (or ejkklhsiva) could have inserted an embolismic Pos, Gam, Anth, or even Elaph once again, but more than one seasonal disruption might appear. 436/5 BCE: SumSol = Day 1 29 Jun AutEqu = Day 93 → → 1 Hek = 1 Pyan = 29 Sep WinSol = Day 181 → = Day 271 → 1 Gam = 1 Moun = Day 366 → Days 179 – 181 24 – 26 Dec 27 Mar SumSol = Days 90 – 93 26 Sep – 29 Oct 26 Dec VerEqu Day 2 1 Jul Days 267 – 270 22 – 5 Mar 1 Hek = 29 Jun Day 357 20 Jun Every Civil Year with this count represents the most difficult to keep aligned. Next 1 Hek arrives nine days before SumSol. Moreover, both AutEqu & WinSol could but would not necessarily fall outside Boid & Pos. VerEqu, on the other hand, still falls in Moun. The basileuv~ (or ejkklhsiva) could have inserted an embolismic month anytime Hek ↔ Anth (in theory), but at least one seasonal disruption would almost certainly appear. 414/3 BCE: SumSol = Day 1 29 Jun AutEqu = → 1 Hek = → 1 Pyan = Day 180 → 1 Gam = Day 92 28 Sep WinSol = = Day 271 → Day 366 → 28 Jun Days 177 – 179 22 – 24 Dec 1 Moun = 25 Mar SumSol = Days 88 – 91 24 -27 Sep 25 Dec VerEqu Day 1 29 Jun Days 265 – 268 19 – 22 Mar 1 Hek = Day 355 17 Jun All Civil Years, which sported this count, represent the most straightforward to have kept aligned throughout an entire Civil Year. Next 1 Hek arrives eleven days before SumSol. More significantly, all three remaining solar events (AutEqu, WinSol, and VerEqu) fall outside their Ordinary Year Civil Months. The basileuv~ (or ejkklhsiva) could therefore have inserted an embolismic Hek, Met, or Boid. The schemas suggest that, during the seventy years 462/1 ↔ 393/2 BCE of the Primer, the basileuv~ (or ejkklhsiva) should have inserted an embolismic Skir nine times, an embolismic Hek six times, an embolismic Elaph five times, and then an embolismic Boid & Pos three times each. If basilei`~ elected merely “to play the odds,” then the baseline months for each range become: CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS SumSol to 1stVisCres Number of Days Embolismic Month 0↔1 II Hek 2↔3 II Boid 4 II Pos 5↔6 II Elaph 7 ↔ 10 II Skir Math challenges a stubborn assumption that has guided Ancient Athenian Calendrical Theory: the basileuv~ (or ejkklhsiva) “regularly” intercalated a 2nd Pos during embolismic years (AYP 160, cf. 368n43). Most deviations during twelve month rolling synodic cycles in fact manifest during Summer. Some begin to appear by Spring, and early-Sum fell during a different Archontic Year than late-Sum. The only attested intercalation that survives from the 5th Century, moreover, indeed inserts II Hek, or lateSummer, not II Pos or mid-Winter (IG I3 73; AYP 382 n. 126). Regardless this exercise represents the (small) first step. Ancient Athenians, for instance, held four grand Panhellenic festivals: Great Panathenaia, Eleusinian Mysteries, Mysteries of Agrai, and City Dionysia. These of course rigorously followed the ancient Attic Civil Calendar, but, to prove manageable thus successful, these four also demanded consistent schedules other povlei~ could follow. In sum, the celebrations could not have simply bounced around the calendar. Precise placement of embolismic months, moreover, becomes more complicated in actual practice than isolated mathematical calculations can show. Today, for instance, one can retroactively correct errors, run various scenarios using different criteria as well as avoid any extenuating circumstances like disruptive sociopolitical events, inclement weather, or even unusually long, short, mild, or severe seasonal climates. Ancient Athenian intercalations must have had “rules,” which took all of the above into account. Schemas Math is everything. Herodotos’ tale of Solon gives 360 day ordinary Civil Years possessing thirty-five intercalations throughout each seventy year period (Hdt. 1.32.2-4). The calculations of Meton, Euktemon et al. presuppose 354 days with seven intercalations inside nineteen years (AYP pp. 51-55, 81-87, 198), and Kallippos determined twenty-eight intercalations inside seventy-six years. Tucked inside Geminos’ account (8.26) are three intercalated years inside every eight (ojktaeteriv~). Censorinus, moreover, notes that Pythagoreans of Philolaos’ time proposed twenty-one intercalations inside fifty-nine years; CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS Demokritos twenty-eight inside eighty-two; and Hipparkhos 112 inside 304 (DN 7.18.8). All of these “schemas” reveal attempts to predict future embolismic years. An observational calendar, on the other hand, remains a different kind of creature. I withdraw my observation of Censorinus (AYP 197): Censorinus DN 7.18.2 Veteres in Graecia civitates cum animadverterent, dum sol annua cursu orbem suum circumit, lunam novam interdum tridecies exoriri idque saepe alternis fieri, arbitrate sunt lunares duodecim menses et dimidiatum ad annum naturalem convenire. Itaque annos civiles sic statuerunt, ut intercalando facerent alternos duodecim mensum, alternos tredecim, utrumque annum separatism vertentem, iunctos ambo annum magnum vocantus; idque tempus trieterida appellabant, quod tertio quoque anno intercalabatur, quamvis biennii circuitus et re vera dieteris esset et cetaera. His explanation (summation) only seems obtuse at first. After further consideration, Censorinus preserves the remnants of just such an observational lunisolar calendar. The critical part: an intercalation would take place every third year (= trieteris) but in two years (= dieteris). Rejecting his math denotes the difference between inclusive and exclusive reckoning, the description becomes truncated or incomplete (corrupt). I propose inserting the words “at times” between the two counts. Double Octaeteris: Allure & Failure Patterns reside in the number of days from SumSol (as reckoned) to the actual appearance of the initial 1stVisCres. By AS a Boö, SumSol should have run (after Meton) 29, 28, 28, 28 Jun and thus the counts-of-days ran (by double octaeteris): 430/29 – 415/4 430 429 428 427 426 425 424 423 422 421 420 419 418 417 416 415 25 13 03 22 11 29 18 08 ------BCE 27 BCE 15 BCE* 04 BCE* 23 BCE 12 BCE 01 BCE 20 BCE 09 BCE BCE BCE BCE BCE BCE BCE BCE Jul O Jul O Jul I Jul O Jul O Jun I Jul O Jul I ------Jul O Jul O Jul I Jul O Jul O Jul I Jul O Jul O 414/3 – 399/8 26 15 5 24 12 1 20 10 | | | | | | | | 414 413 412 411 410 409 408 407 28 17 6 25 13 3 22 11 | | | | | | | | 406 405 404 403 402 401 400 399 29 17 06 25 14 02 21 11 --------BCE 30 BCE 18 BCE 08 BCE 27 BCE 16 BCE 04 BCE 22 BCE 12 BCE BCE BCE BCE BCE BCE BCE BCE Jul I Jul O Jul I Jul O Jul O Jul I Jul O Jul O -------Jun I Jul O Jul I Jul O Jul O Jul I Jul O Jul O 1 19 8 27 15 4 23 13 1 20 10 29 17 6 24 14 CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS “*” = Chap XX, pp xxx-xxx. It goes without saying that the dates represent how the years ought to have run (cf. AYP 178 Table 10, 185-187 viz. Table 16). Buried in the above jumble of numbers reside sequences. The first pattern, or perhaps the most noticeable one, begins with the intercalation of 423 BCE. The 1stVisCres fell ten days after SumSol. A repeating countdown then appears with each subsequent intercalation: 10 6 3 1 - 8 4 1 - 10 6 4. The next pattern reflects this one. The first ordinary years that follow then run 28 25 22 19 - 27 23 20 - 29 24. Finally, the second ordinary years after intercalation too possess a sequence, though they become interrupted: 17 13 11 * - 15 13 * - 17 14. The sequences simply stand incomplete. The double octaeteris falls short to unlock how cyclical movements of the Moon repeat against SumSol. The range needs extended. Meton, Euktemon et al., for example, discovered the Moon against the Sun “resets” by conjunction every nineteen years (e.g., 411 BCE ff. mirrors 430 BCE ff. mirroring 449 BCE ff). We shall go seventy. By AS a Boö (before Meton), the number of days from SumSol (as reckoned) to actual appearance of 1stVisCres ran from 30, 29, 29, 29 Jun. Consequently, numbers in parantheses denote the counts as if SumSol had reckoned by 29, 28, 28, 28 Jun. Expanding upon the previous table (again by double octaeteris): 462/1 – 447/6 462 461 460 459 458 457 456 455 454 453 452 451 450 449 448 447 19 Jul 07 Jul 26 Jul 16 Jul 05 Jul 23 Jul 12 Jul 01 Jul -------BCE 20 Jul BCE* 08 Jul BCE* 27 Jul BCE 17 Jul BCE 07 Jul BCE 25 Jul BCE 14 Jul BCE 03 Jul BCE BCE BCE BCE BCE BCE BCE BCE 398 BCE 397 BCE 396 BCE 02 Jul 20 Jul 09 Jul 446/5 – 431/0 O 19 (20) 446 BCE 22 Jul I 8 (9) 445 BCE 10 Jul O 27 (28) 444 BCE 29 Jun O 17 (18) 443 BCE 18 Jul I 5 (6) 442 BCE 08 Jul O 24 (25) 441 BCE 26 Jul O 13 (14) 440 BCE 16 Jul I 2 (3) 439 BCE 05 Jul --------------O 20 (21) 438 BCE 24 Jul I 9 (10) 437 BCE 12 Jul O 28 (29) 436 BCE 01 Jul O 18 (19) 435 BCE 20 Jul I 7 (8) 434 BCE* 09 Jul O 26 (27) 433 BCE* 28 Jul O 15 (16) 432 BCE 17 Jul I 4 (4) 431 BCE 07 Jul ----------------------------------------------------I 3 395 BCE 29 Jun O 22 394 BCE 17 Jul O 11 393 BCE 05 Jul O 22 O 11 I 0 O 19 I 8 O 27 O 17 I 6 -------O 24 O 13 I 2 O 21 I 9 O 28 O 18 I 9 I O I (23) (12) (1) (19) (9) (28) (18) (7) (25) (14) (3) (22) (10) (29) (19) 1 19 7 “*” = years Meton’s revisions would have resulted in intercalation changes, i.e., 453/2 & 434/3 BCE should run CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS ordinary with 452/1 & 433/2 BCE embolismic (both years = 28 Jun & 0). In any case, the patterns of days SumSol ↔ 1stVisCres over the seventy years covered by the Primer ran (note: bracketed numbers [#] = what should have happened): a) intercalated: b) 1st ordinary: 9 6 3 [0] – 8 4 1 – 9 7 3 [0] – 9 5 1 – 10 6 3 1 – 8 4 1 – 10 6 4 [1] 28 25 21 [19] – 27 23 19 – 28 25 22 [19] – 26 24 20 – 28 25 22 19 – 27 23 20 – 29 24 22 [19] When the next set expands, however, the “interruptions” shift throughout: c) 2nd ordinary: [*] 18 14 [10] – [*] 16 12 – [*] 18 14 [10] – [*] 15 12 – [*] 17 13 11 – [*] 15 13 – [*] 17 14 11 Interestingly, the ordinary years “sandwiched” between two intercalated years can also complete the third sequence and thus “fill the gaps:” c) 2nd ordinary: [20*] 18 14 [10] – [19*] 16 12 – [19*] 18 14 [10] – [19*] 15 12 – [20*] 17 13 11 – [19*] 15 13 – [20*] 17 14 11 All three sequences run 4 3 4 3 4 3 4. Within the pattern, embolismic years alternate between every third and second years [3] 1 2 1 [3] 1 2 1 3 1 2 1 3 1. This final pattern in fact appears to indicate what Censorinus meant when differentiating between the trieteris and dieteris. At this point, the primary interval into which ancient Greeks attempted to apply these patterns became the ojktaethriv~, but buried inside this particular range was the smaller pentaethriv~ or quadrennium. Ancient Greeks discovered two oddities: 1) occasionally, three intercalations did not occur during an ojktaethriv~; and 2) the precise placement of embolismic years change (or rather rotate) within quadrenniums over time (L → R). 462/1 454/3 446/5 438/7 430/29 422/1 414/3 406/5 398/7 → → → → → → → → → 455/4 BCE: 447/6 BCE: 439/8 BCE: 431/0 BCE: 423/2 BCE: 415/4 BCE: 407/6 BCE: 399/8 BCE: [391/0] BCE: OIOO O[OI]O OOIO OOIO OOIO OOIO IOIO IOIO IOOI IOOI IOOI IOOI OIOI OIOI OIOO OIOO OIOO OI[OO] Beginning with the Great Panathenaia year of 462/1 BCE, and running through 387/6 BCE, as well as following a SumSol reckoned throughout on 29, 28, 28, 28 Jun, each year’s Hekatombaion noumhniva would have produced the following sequences that read as a “countdown of days” (Read: L → R): CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS -- -- 4*] [28 18 6*] [27 16 5] [28 18 7] [26*15 5] [28*17 6] [27 15*4] [29 17*6] [28 15 4*] [23 12 1] [25 14 3] [23*12 1] [25*14 3] [24 12*1] [{25}13*3] [23 13 1*] [24 14 4*] [23 13 1] [20* 9] [21*10 {0}] [20 9*] [22 10*{1}] [20 10] [22 11 1*] [20 10] [22 11 1] k.t.l. [19 8*] [19 9] [19 8] [19*7] “*” = Great Panathenaia year; {#} = what should have unfolded. As expected, each set of numbers advance (or drift) toward SumSol. The intervals unfold either in two sets of three years then one set of two years or three sets of three years and one set of two years. Both patterns repeat at consistent intervals but in effect “reset” each time 1stVisCres fell less than ten but more than four days after SumSol. Additionally, eight years (ojktaethriv~) indeed comprise and complete any two sets of three years and one set of two years (in any combination). Moreover, sixteen years (duoeidhv~ ojktaethriv~) will comprise and complete if the count begins with any set of two years or with any three year set that falls just prior to a two year set (in any combination). The Problem: neither eight nor sixteen year counts of any combination continue beyond three rotations. The sequence for intercalations then shifts by one year. Let us contrast these counts against Olympiad ojktaethrivdo~. The overall pattern should remain the same, i.e., still possessing the eight and sixteen year sequences. The question thus becomes do the numbers change much if the starting year changes. 464/3 456/5 448/7 440/39 432/1 424/3 416/5 408/7 400/399 → → → → → → → → → 457/6 449/8 439/8 431/0 425/4 417/6 409/8 401/0 393/2 BCE: BCE: BCE: BCE: BCE: BCE: BCE: BCE: BCE: OIOI OIO[O] OIOO OIOO OIOO OIOO OOIO OOIO OOIO OOIO [I]OIO IOIO IO[OI] IOOI IOOI IOOI IOOI OIOI Beginning Ol. 79.1, i.e., the ancient Attic Archontic Year when those Olympian Games took place, and running from 464/3 BCE through 393/2 BCE, as well as following a SumSol reckoned throughout on 29, 28, 28, 28 Jun, each year’s Hekatombaion noumhniva produces the following sequences that read as “countdowns.” Note: the years overlap with the Great Panathenaia CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS beginning with the initial countdown. This starts with the 3rd count of 20 days (again, read L → R): [28*18 6] [27 16*5] [28 18*7] [26 15 5*] [28 17 6*] [27 15 4] [29 17 6] --- 12*1] [24 14*3] [23 12 1*] [25 14 3*] [24 12 1] [{25}13 3] [23*13 1] [24*14 4] [20 9] [21 10 {0}*] [20 9] [22 10 {1}] [20*10] [22*11 1] [20 10*] [22 11*1] [19 8] [19*9] [19 8*] [19 7] ktl. “*” = an Olympic Game year; {#} = what should have unfolded. As expected, each set for Olympiad ojktaethrivdo~ that advance (or drift) toward SumSol effectively follows the same pattern witnessed for the Panathenaiad ojktaethrivdo~. Once again, eight years (ojktaethriv~) indeed comprise and complete any two sets of three years and one set of two years (in any combination), while sixteen years (duoeidhv~ ojktaethriv~) will comprise and complete if the count begins with any set of two years or with any three year set that falls just prior to a two year set (in any combination). Both series present unavoidable consequences. A Great Panathenaia had taken place during or immediately following an intercalated year 1, 5, 9, 13, 17, 21, 25, 29, 37, 45, 53, 61, 69, 73, and 77, i.e., all except 33, 41, 49, 57, and 65. The Olympian Games, moreover, would have taken place during or immediately following an (Attic) intercalated year 5, 13, 21, 29, 33, 37, 41, 45, and 49 (and also applied to 57). Panhellenic panhvgurei, in sum, raise a myriad of complications (and hurdles) for how ancient Athenians (and by extrapolation all ancient Greek povlei~) determined intercalations, while also accounting for (reckoning) events that affected multiple povlei~. Excursus: Panhellenic Festivals Ancient Greeks in fact gathered from all over the Hellenes to celebrate four grand ajgw`ne~: two every four years (or rather on every fifth year) and two every other year (or rather on every third year). b More importantly, however, their individual schedules resulted in at least one gathering taking place every single year whether reckoned, for instance, by the ancient Athenian Calendar(s) or by the ancient Roman Julian Calendar. In addition, ancient Athenians held three annual “Panhellenic” b) Other such festivals, in addition to the Great Panathenaia, took place, e.g., the Grand Eleusinia (every fifth year) & the Delia (every sixth year). CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS gatherings: the Eleusinian Mysteries, the Mysteries of Agrai, and the Dionysia Asty. In essence, ancient Greeks gathered for Panhellenic celebrations at different locations every single year and more than once throughout any given year. The difficulties faced to schedule such gatherings successfully for any society, where instantaneous communication did not (and could not) exist, become rather apparent rather quickly. In short, if the host povli~ capriciously invoked an embolismic year, which abruptly “dislocates” a Panhellenic gathering a whole synodic cycle, then the festival could not have remained readily determined in a consistent (or expected) manner. For example, the Mysteries of Eleusis always began on the fifteenth day of the Attic Civil Month Boedromion. During Ordinary Civil Years, this astronomically translates as “under a waning Full Moon that appears around AutEqu.” The immediate (and most basic) question: how would ancient Greeks from other povlei~ know whether this meant the closest waning Full Moon before or after VerEqu? Or, if the basileuv~ had “bumped” it? The Great Panathenaia, on the other hand, always culminated trivth fqivnonto~ Hek = first New Moon Conjunction that followed the initial 1stVisCres after SumSol. All successful Panhellenic panhvgurei must have followed a similar type of reckoning. This particular portion of the discussion continues Chap. XX, pp. xxxxxx through Chap. XX, pp. xxx-xxx. Accurate Alignments One rather important conclusion reached in the Primer: for ancient Greeks, Solstices & Equinoxes did not (existentially) represent precise moments in time but rather finite periods of time. Solstices, for instance, appear to align up to five consecutive solar days that possess indiscernible differences, while Equinoxes possess at least two such solar days (AYP 149-157). If one takes into account further that an ancient Greek hJliotrovpaion undoubtedly possessed not negligible margins-oferror, then ambiguities and uncertainties abound. Regardless, for lunisolar calendars to function properly, every astronomical event required a specific day or a finite set of days. Through nothing more than running numbers by trial-anderror, which eventually resulted in a serious stack of discarded spreadsheets, I eventually concluded that Meton, Euktemon, et al. indeed successfully (and correctly) identified 28 Jun as SumSol of 432 BCE. I still consider this a stunning achievement. c c) Primarily because I refused to accept they could have measured Helios correctly. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS A major assumption, however, must come into play. Meton, Euktemon et al. duplicated (or had already accomplished) the same fete for WinSol, and this effort has simply dropped from the historical record. In any case, with both solstices in place, determining each equinox then became matters of confirming measurements and supportive math. By 430 BCE (allowing for maturation and saturation of the discovery), ancient Athenian astronomers ought have accepted, and thus the basileuv~ (and ejkklhsiva) ought have reckoned AutEqu on 28 Sept; WinSol on 25 Dec; VerEqu 26 Mar; and SumSol on 28 Jun (in seasonal order). This represents one of two separate achievements by Meton et al. (Chap. XX, pp. xxx-xxx). By 341 BCE, however, both AutEqu & WinSol had begun drifting into 27 Sept & 24 Dec, while VerEqu & SumSol had (for the most part) drifted primarily into 25 Mar & 27 Jun. The 4th Century BCE, however, does not present an insurmountable problem with how ancient Greek may have determined dates. As late as 335/4 BCE, for instance, SumSol still occasionally fell on 28 Jun (03:52:42±), VerEqu on 26 Mar (01:37:38±), and AutEqu on 28 Sept (02:34:37±), i.e., by modern delineations, which use midnight to advance solar days. The questions now become how rigorous subsequent measurements became and then the margins-of-error they realized. If a “typical” ancient Greek gnwvmwn from the pre-Hellenistic era possessed measurement errors in the neighborhood of ±3 solar days (AYP 149-157), then seasonal reckonings should have become a matter of convention and tradition rather than, when conducted, meticulously noting the differences produced by any subsequent measurements (AYP 352 Spreadsheet XLII). The operative response, in other words, would have become the ancient Greek equivalent of “meh, close enough.” On the other hand, when driven ancient astronomers after Meton & Euktemon (e.g., Kallippos) conducted their own observations and made calculations, discrepancies uncovered would (in all likelihood) become corrections. More bluntly, later astronomers concluded previous astronomers had erred. Helios therefore never really moved away from the stars; the (retroactively applied) math moved previous attempts closer to the correct number, i.e., until ongoing measurements began drifting outside all possible margins-of-error. Additionally, once Meton et al. had established the “official” dates for both solstices and both equinoxes, ancient Athenians then deferred to the star Arktouros to regulate the four solar CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS events (AYP 157-159). While nowhere attested in ancient sources, stipulated, the math appears unassailable (e.g., The Choiseul Marble). These eight important dates then remained in place until evidence Helios deviated from Arktouros accumulated. The phenomenon practically forced Hipparkhos to unlock solstices and equinoxes. As a result, by 127 BCE, he discovered Helios indeed shifted against the stars (AYP 383n133). d A related assumption, however, retroactively applies: Meton, Euktemon, et al. had also corrected for what they concluded represented (traditional) errors in reckoning. Ancient Greeks (or at least ancient Athenians) had positioned solstices & equinoxes at least one solar day too late. From the shift, their nineteen year cycle emerged. This discussion will continue Chap. XX, pp. xxxxxx. Their efforts, moreover, “to correct” the astronomical calendar emerged from “The Problem of 434/3 BCE.” This discussion continues Chap. XX, pp. xxx-xxx. Complications When apparent alignments between Selene’s 1stVisCres and Helios’ Solstices & Equinoxes occurred, precision ultimately proves less consequential than presumed. This began as one of the most difficult premises for me to accept. The finding, however, does not apply so much to ancient Attike in isolation but rather when considering ancient Attike against the rest of the ancient Hellenes and vice versa. Even though the present author holds ancient Greek astronomers, and certainly ancient Athenian astronomers, grew quite adept predicting on what solar day a 1stVisCres would indeed appear, by no later than the immediately preceeding 3rdQ, the possibility (and I would argue probability) exists that other povlei~ not only used more formulaic calendars (e.g., ancient Sparta [AYP 268-273]), e but that other povlei~ had also come to use different phases of the Moon. Other ancient Greeks, for instance, certainly used WinSol and equinoxes. Additionally, simply because Meton, Euktemon, et al. reckoned AutEqu 28 Sept; WinSol 25 Dec; VerEqu 26 Mar; and SumSol 28 Jun, and (as argued) convinced ancient Athenians to d) By ca. 170 BCE, manufacturing techniques and technology had apparently advanced enough so that Hipparkhos came to suspect (at least) VerEqu did not follow sidereal solar reckoning. He thus began duplicating the efforts of Meton, Euktemon, et al. His recorded observations and calculations, moreover, reveal a mean dec(d) error of +7 min (i.e., the sum of atmospheric refraction & parallax). Regardless, the Tropical Solar Year had come into existence forever changing our understanding of the heavens. e) See also Chap. XX, pp. xxx-xxx CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS adopt these dates, non sequitur the rest of ancient Greece accepted them. “Ambiguities” (for lack of a better term) therefore always existed. Ancient Greeks had nonetheless adapted and (successfully) overcame these problems to create a plethora of different yet regionally functional lunisolar calendars. The Methodology The solution is absurdly counterintuitive. To re-align the lunar calendar with its parallel solar year requires two ambiguous astronomical events to converge. This means specifically that the precise solar days remained difficult to determine by observation. Solstices & Equinoxes (mevn) had always proven ambiguous. For the Moon (dev), every phase but the 1stVisCres & FinVisCres had also proven at least somewhat ambiguous. Specifically, Selene constantly changes shape in the sky. Thus (mevn), she indeed produced phases, which appeared the same on the same days across the entire Hellenes, but (dev) the shape required judgement calls based on nothing more than simple lineof-sight. One ancient Greek opining the Moon had reached 25% or 50% illumination became another ancient Greek’s opinion of “not yet” or “too late” (AYP 145-149). I see no way to avoid drawing this most rudimentary of inferences. f To keep the present argument manageable, we shall assume that all such judgement calls possessed margins-of-error of (at most) ±2 Solar Day between different povlei~, i.e., a ¼, 1stQ, Full, 3rdQ, ¾, and New Moon always reckoned within two solar days of each other throughout the Hellenes regardless of the regional judgments made or the lunisolar methodology followed. The FinVisCres, on the other hand, always vanished on a specific day; the following 1stVisCres then always appeared on a specific solar day. Both days remained exact whether or not predicted accurately or accurately rendered by some formula. The key “ambiguous” astronomical event thus rested between the two. The New Moon provides a “window” of roughly three Solar Days. The 1stVisCres undoubtedly marked noumhniva for every Attic Civil Month, but, following the presented line-of-reasoning, Ancient Athenians in fact based their ancient Attic Archontic (Civil) Calendar on both solstices and both equinoxes against four f) No student of ancient Athenian Calendars should use me as a barometer, but the more I have watched the Moon, the more I understand too many variables exist to conclude definitively how ancient Greeks from different povlei~ determined lunar reckonings. Observations made, for example, around Nautical to Astronomical Twilight at dusk can differ from those made around Astronomical to Nautical Twilight at dawn. I remain convinced, however, that each povli~ possessed an “official” platform. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS of twelve regularly repeating New Moons, i.e., ancient Attic Impure Days (see previous Chap.). Specifically, during all Ordinary Civil Years, the counts of days between these sixteen baseline astronomical events ran consistently against each other without producing convergences. When two of these “ambiguous” astronomical events, i.e., one solar and one lunar, did converge, however, ancient Athenian astronomers then artificially reckoned one or the other (but not both) as unambiguous. In other words, they assigned one of them to a specific day. In theory, ancient Athenian astronomers could have kept the solstices and equinoxes ambiguous against a precise Conjunction, or they could have used the ambiguous New Moon against precisely reckoned solstices and equinoxs. Both methodologies will typically but not always produce the same results to determine seasonally accurate intercalations as long as each followed essentially the same underlying premise. For example, if ancient Greeks considered solstices and equinoxes lasted, say, three solar days, then the “benchmark” 1stVisCres must appear after the final day of the solstice or equinox in question. Conversely, if a New Moon lasts three days, then the solstice or equinox in question must fall during them. Both rules would effectively force the “calibration” 1stVisCres beyond the solstice or equinox. Once again, math becomes everything. Ancient Attic Archontic Months (and by extrapolation all ancient Greek Lunar [Civil] Months] represented specific Synodic Cycles that ought arrive before, run through, or begin after a particular solstice or equinox. For example, if Synodic Cycle I began before but ended after SumSol, then Synodic Cycle IV would begin before but end after AutEqu. Synodic Cycle VII would then begin before and end after WinSol, and Synodic Cycle X before and after VerEqu. Consequently, in ancient Attike, during Ordinary Civil Years, Hek (ought) always equate to the first complete Synodic Cycle that began and ended after SumSol (or Synodic Cycle II); Pyan (ought) always equate to the first complete Synodic Cycle, which began and ended after AutEqu (or Synodic Cycle V); Gam (ought) always equate to the first complete Synodic Cycle that began and ended after WinSol (or Synodic Cycle VIII); and Moun (ought) always equate to the complete Synodic Cycle, which began and ended after VerEqu (or Synodic Cycle XI). As Lunar Years advanced against the Sidereal Solar Year, thus drifted outside these seasonal alignments, the inevitable shift that approached demanded an adjustment. Scholars (including CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS this one), however, have erred on the purposes embolismic months served. An intercalation in fact possessed two different applications: one in practice and then a second in purpose. Everyone focuses on the former. As mentioned above (p. xxx), the Primer did not address whether the four key seasonal events should fall within the nominal ordinary month (AutEqu = Cycle III [Boid]; WinSol = Cycle VI [Pos]; VerEqu = Cycle IX [Elaph]; and SumSol = Cycle XII [Skir]) or could just as readily fall during its embolismic month. The decision here dictates placement of the intercalation. If ancient Athenians did not consider a Civil Year seasonally aligned when key solar events fell within Month III2, VI2, IX2, or XII2, then the intercalated month must insert before Month III, VI, IX, or XII. This restriction, however, creates the alignment problems explored. The second option, on the other hand, makes the first one an unnecessary conundrum. The two posited “meanings” of an intercalation rather complement each other. An embolismic month existentially represented an additional, or, more specifically, a thirteenth, synodic cycle between two occurrences of the same solar event (e.g., SumSol ↔ SumSol or VerEqu ↔ VerEqu). This becomes the practical application. Conceptually, however, each intercalation produced an “elongated” Civil Month. This was the purpose. The month in question became comprised of two consecutive synodic cycles. It now possessed a) two sets of ten waxing days; b) two sets of ten middle days; and finally c) two sets of (up to) ten waning days. The Civil Month, in effect becomes one running 58 ↔ 60 days All “problematic alignments” now promptly vanish. The findings not only challenge my proposed Civil Calendar Rules e (Chap. X, p. xx) but also one of the most fundamental assumptions accepted today: 1 Hek could fall on SumSol. Outside observational or calculation errors, which undoubtedly occurred time-to-time, such an alignment ultimately proves untenable to maintain an effectively functional lunisolar calendar precisely because of the problematic math it produces. g A 1stVisCres therefore determined when an ancient Athenian Civil Month began, not to mention the next Archontic Year, but its appearance did not determine the proper placements of intercalations. This duty deferred to the immediately preceeding g) I have set aside Prof. Pritchett’s more extreme skepticism. By extrapolation, the observation also means 1 Boid should not fall on AutEqu, 1 Pos on WinSol, and 1 Elaph on VerEqu. Even though some of these alignments would prove mathematically impossible depending when 1 Hek fell after SumSol, the principle stands. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS New Moon. Ancient Athenians, in other words, used this small but adequate “window” into which the four ambiguous solstices and equinoxes would at times fall to their advantage. For example, the exact days the four key solar events fell (mevn) may or may not have proven correct. I proposed, for instance, that all measurements inherently possessed a margin-of-error of approx. three solar days. Similarly (dev), at least some povlei~ in all probability reckoned solstices and equinoxes on different days. Sans utter indifference or incompetence, these too should not have differed more than (at most) three solar days. Assuming both inferences sound, then, by using an ambiguous astronomical event, either a solstice or equinox lasting three days or a Moon phase of three days, the differences ultimately become immaterial or at least substantially less relevant to calculate and place an Embolismic Civil Month. h Adjusted Math This new hypothesis for New Moons and Embolismic Civil Years affects the math for years 445/4 ↔ 444/3; 434/3 ↔ 433/2; 423/2 ↔ 422/1; and 415/4 ↔ 414/3 BCE as well as (possibly) the years 453/2 ↔ 452/1; 426/5 ↔ 425/4; 407/6 ↔ 406/5; and 396/5 ↔ 395/4 BCE. Note: Julian Date = 1 Hek; First “#” = days after SumSol when reckoned 30, 29, 29, 29 Jun; Second “(#)” = days after SumSol when reckoned 29, 28, 28, 28 Jun; Years listed by ojktaethriv~. 462/1 – 447/6 462 461 460 459 458 457 456 455 BCE BCE BCE BCE BCE BCE BCE BCE 454 453 452 451 450 449 448 447 BCE BCE BCE BCE BCE BCE BCE BCE 19 Jul 07 Jul 26 Jul 16 Jul 05 Jul 23 Jul 12 Jul 01 Jul -------20 Jul 08 Jul 27 Jul 17 Jul 07 Jul 25 Jul 14 Jul 03 Jul O 19 I 08 O 27 O 17 I 05 O 24 O 13 I 02 -------O 20 I 09 O 28 O 18 I 07 O 26 O 15 I 04 446/5 – 431/0 (20) (09) (28) (18) (06) (25) (14) (03) | | | | | | | | 446 445 444 443 442 441 440 439 BCE BCE BCE BCE BCE BCE BCE BCE (21) (10) (29) (19) (08) (27) (16) (04) | | | | | | | | 438 437 436 435 434 433 432 431 BCE BCE BCE BCE BCE BCE BCE BCE 22 Jul 10 Jul 29 Jul 18 Jul 08 Jul 26 Jul 16 Jul 05 Jul -------24 Jul 12 Jul 01 Jul 20 Jul 09 Jul 27 Jul 17 Jul 07 Jul O 22 I 11 O 30 O 19 I 08 O 27 O 17 I 06 -------O 24 O 13 I 02 O 21 I 09 O 28 O 18 I 08 (23) (12) (31) (19) (09) (28) (18) (07) (25) (14) (03) (22) (10) (29) (19) (09) h) Unless, of course, reckonings indeed differed more than three solar days. Such a spread, however, seems unlikely. The Olympian Games, for instance, had used SumSol since the 8th Century BCE. Three centuries becomes time enough to agree. Chap. XX, pp. xxx-xxx. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS Note: At this point, each ojktaethriv~ follows from Meton’s et al. adjustments (Chap. XX, pp. xxx-xxx). Julian Date = 1 Hek; First “#” = days after SumSol when reckoned 29, 28, 28, 28 Jun. See Chap. XX, pp. xxx-xxx for the years 420/19* & 419/8* BCE. I shall go ahead and finish the ninth ojktaethriv~ 430/29 – 415/4 430 429 428 427 426 425 424 423 422 421 420 419 418 417 416 415 414/3 – 399/8 25 Jul O 26 | 414 BCE 28 Jul O 13 Jul O 15 | 413 BCE 17 Jul O 03 Jul I 05 | 412 BCE 06 Jul I 22 Jul O 24 | 411 BCE 25 Jul O 11 Jul O 12 | 410 BCE 14 Jul O 29 Jun I 01 | 409 BCE 02 Jul I 18 Jul O 20 | 408 BCE 21 Jul O 08 Jul I 10 | 407 BCE 11 Jul O ---------------------------BCE 27 Jul O 28 | 406 BCE 30 Jun I BCE 15 Jul O 17 | 405 BCE 18 Jul O BCE* 04 Jul I 06 | 404 BCE 08 Jul I BCE* 23 Jul O 25 | 403 BCE 27 Jul O BCE 12 Jul O 13 | 402 BCE 16 Jul O BCE 01 Jul I 03 | 401 BCE 04 Jul I BCE 20 Jul O 22 | 400 BCE 22 Jul O BCE 09 Jul I 11 | 399 BCE 12 Jul O -----------------------------------------------------------------I 03 398 BCE 02 Jul 397 BCE 20 Jul O 22 396 BCE 09 Jul O 11 395 BCE 29 Jun I 01 394 BCE 17 Jul O 18 393 BCE 05 Jul I 07 392 BCE 25 Jul O 27 391 BCE 14 Jul O 16 BCE BCE BCE BCE BCE BCE BCE BCE 30 19 08 27 15 04 23 13 01 20 10 29 17 06 24 14 The adjusted counts of days (i.e., the post-Meton shift) for a SumSol ↔ 1stVisCres sequence that instead follow the New Moon hypothesis for the seventy-two years run: a) intercalated: b) 1st ordinary: c) 2nd ordinary: 9 6 3 – 10 8 4 – 12 9 7 3 – 10 9 5 1 – 10 6 3 – 11 8 4 1 – 10 6 3 1 - 7 28 25 21 – 29 27 23 – 31 28 25 22 – 29 26 24 20 – 28 25 22 – 30 27 23 20 – 29 24 22 18 - 27 18 14 – 19 16 – 19 18 14 – 19 15 12 – 17 13 19 15 13 – 17 14 11 - 16 Once again, expanding the second ordinary year after intercalation to include those quadrenniums, which did not possess one, those sequences run: d) 2nd ordinary: 18 14 – [21] 19 16 – [23] 19 18 14 – [22] 19 15 12 – [20] 17 13 - [22] 19 15 13 – [20] 17 14 11 – [18] 16 CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS All three sequences do not in fact alternate 4 3 4 3 4 3 4 but rather 4 4 3 4 4 3 4 4. Within this pattern, embolismic years do not alternate between every third and second years [3] 1 2 1 [3] 1 2 1 3 1 2 1 3 1 but rather 2 1 2 1 3 1 2 1 2 1 3 1. In sum, the earlier sequences represent “true” Synodic Cycle counts, while these new sequences represent Civil Month designations. Such determinations, however, followed from constant and continuous astronomical observations. Predicting what would happen during the current synodic cycle or during the current seasonal year proves an entirely different undertaking than predicting what might happen several years in advance. Put another way, understanding next year would run embolismic became considerably less daunting than predicting how many embolismic years would exist during the next sixteen. Most ancient Greeks (dev) undoubtedly lived by the former; ancient Greek astronomers (mevn) sought to unlock the latter. Sitting silently behind the present analysis, moreover, rest the (so far) briefly mentioned Panhellenic celebrations. Had ancient Greeks not held such gatherings, accurate lunisolar calendars would have remained far less consequential for any povli~ in question. Ancient Athenians, as stressed, hosted four such gatherings. These of course remained subject to the ancient Attic Archontic Calendar but also impacted other povlei~. The logic also flows in reverse. How much consideration would ancient Athenians have given to the Olympian, Pythian, Isthmian, and Nemeian Games? Did it matter during which ancient Attic Archontic Month these took place? Once again, this particular discussion continues Chpts. XX-XX, pp. xxx-xxx. Conclusions Four criteria became recognized and eventually manipulated so ancient Athenians could invoke embolismic years effectively. The methodology that positioned all ancient Attic Archontic intercalations emerged from: 1) The SumSol’s exact alignment remained ambiguous but still required a specific day assigned; 2) The three other key solar events (AutEqu, WinSol, VerEqu), though ambiguous as well, nevertheless also required specific days assigned; 3) The occasional alignments between these solar events and New Moons dictated the count of Synodic Cycles; 4) All Panhellenic Celebrations demanded consistent schedules to prove not only successful but simply functional. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS We shall set aside #4 until Chpts. XX-XX, pp. xxx-xxx. For now, however, the basic principles that guide intercalations also apply to Panhellenic celebrations: to gather again from all over the Hellenes, each panhvguri~ must have aligned to a specific Synodic Cycle in relation to a solar “anchor,” i.e., an event like a solstice, equinox, or the rising/setting of a star. The two questions, which remain, become a) “how” and then b) does “specific Synodic Cycle” = “particular Civil Month.” In any case, the first three criteria almost assuredly evolved over a not insignificant period of time. Attempts to make sense of the sky, moreover, and then use it to establish order for ancient Greek daily lives, had become (partly) established (at least) as far back as Hesiodos and Homeros. In ancient Attike, the calendrical reforms introduced by Solon suggest capabilities had advanced far enough to follow the methodology proposed here. Meton, Euktemon, et al. then refined ancient Athenian astronomers’ understanding of the sky further by uncovering the nineteen year “reset.” At that point, ancient Greek astronomers (figuratively speaking) went “off to the races.” Looking at the whole intercalation methodology from the other side of the equation, inserting an embolismic month seasonally too early or too late or advancing or retarding lunisolar years by omitting an anticipated intercalation or inserting unnecessarily an additional embolismic month all came with considerable costs. Each scenario displaces or disrupts seasonal alignments for all subsequent Civil Months that follow. The Anthesteria, for instance, ought take place when ancient Athenians opened the season’s wine vats (AYP 237 n. y; Chap. XX, pp. xxx-xxx). In addition, “wayward intercalations” could “bump” any of the four ancient Attic Panhellenic gatherings (Great Panathenaia, Eleusinian Mysteries, Mysteries of Agrai, and the City Dionysia). Three of these festivals, moreover, also represented decidedly seasonal events. Unexpected or skipped intercalations could also shift any of the expected ancient Attic monthly alignments for the Olympian, Pythian, Nemeian, and Isthmian Games. Each of these complications represent formidable hurdles that, quite bluntly, a basileuv~ or ejkklhsiva could not flippantly ignore. I do not, however, arrogantly presume ancient Athenians never omitted a scheduled intercalation nor ever inserted an additional embolismic month. I seek rather only to stress that such actions should ultimately prove extremely rare. The latter certainly took place 190/89 → 189/8 BCE (IG II/III3 1, 1268-1271, 1273-1274; AYP 223-237), and the former (probably) took place 420/19 → CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS 419/8 BCE (Antiph. 6.44-45; AYP 185-186). i When uncovered epigraphic evidence therefore reveals such disruptive deviations actually occured, the question promptly becomes (or ought to become) “why.” One hypothesis, for instance, which I have proposed as a possibility: exceptional seasonal weather like an unusually long and harsh Winter. Such an event would have affected most if not all of the Hellenes and could have thus “forced” an extra intercalation to keep the Spring sailing season as well as the (now delayed) Summer harvests aligned within the ancient Archontic Calendar (for a possible example in Thoukydides, see Chap. XX, pp. xxx-xxx). Finally, at the risk of repeating a point ad nauseam, different magistrates down through the centuries probably held different opinions on what represented the optimal (or most prudent) courses of action to take. Other magistrates, moreover, may have faced unheard circumstances. Regardless, they each at times certainly faced different situations. Additionally, societies evolve. Prerequisites change. Any driving considerations in play thus move. What may have worked during the 5th & 4th Centuries BCE, for example, may not have been prudent by the 2nd Century BCE. j Example: if the author’s hypotheses regarding the significance of the Apatouria to establish a) every ancient Athenian’s politeiva and then b) every ancient Athenian’s (legal) age to claim that politeiva proves sound (Chpts. XX-XX, pp. xxx-xxx), then the festival’s seasonal alignment to late-Fall ↔ early-Win (Pryt. III ↔ IV) possessed considerable cultural significance. At some point during the 3rd Century, however, practically all mentions of this festival drop from the historical record. This could reveal a simple accident of history, or it shows that the Apatouria had in fact lost its significance. Consequently, the necessary seasonal alignment dimishes perhaps even vanishes. 14 The common denominator nonetheless always remained: the ancient Athenian Calendars required following the Moon to the best of their abilities. i) See also Chap. XX, pp. xxx-xxx j) Although cumbersome to illustrate with specific examples, the never-ending and unresolved feud(s) between Profs. Meritt & Pritchett reveal they both (at times) overlooked this very real possibility. Just because some action taken during Century X exists does not ipso facto mean it ought also apply to Century Y. In essence, watching and following the sky always took place; the variable(s) became the decisions that followed at the time(s) a judgment call became required. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS Table X: 462/1 to 433/1 BCE Julian Year Civil Intercalation Hek. 1 Number of Days 462/1 461/0 460/59 459/8 458/7 457/6 456/5 455/4 454/3 453/2 O IS O O V I S O O S I A O V I S 19 July 07 July 26 July 16 July 05 July 23 July 12 July 01 July 20 July 08 July 354 384 355 354 384 354 354 384 354 384 O O IS O O V I S O V I S O O 27 July 17 July 07 July 25 July 14 July 03 July 22 July 10 July 29 July 18 July VI S 08 July 26 July 16 July 05 July 24 July 12 July 1 July 20 July 09 July 27 July 452/1 451/0 450/49 449/8 448/7 447/6 446/5 445/4 444/3 443/2 442/1 441/0 440/39 439/8 438/7 437/6 436/5 435/4 434/3 433/2 V V O O VI S O O S I A O V I S O Calendar Equation Pryt. I.1 Number of Days Conciliar Intercalation Calendar Equation Full / Hollow = Pryt I.16 = Pryt I.05 = Pryt I.24 = Pryt I.14 = Pryt I.02 = Pryt I.21 = Pryt I.10 = Pryt X.34 = Pryt I.17 = Pryt I.06 4 July 3 July 3 July 3 July 4 July 3 July 3 July 3 July 4 July 3 July 365 365 365 366 365 365 365 366 365 365 O O O I O O O I O O = Skir 16 = Skir 27 = II Skir 7 = Skir 18 = Skir 29 = Skir 10 = Skir 21 = Hek 03 = Skir 14 = Skir 25 F (+) H (-) H (-) F (+) H (-) H (-) H (-) [H (-)] H (-) H (-) 355 355 384 354 354 384 354 384 354 355 = Pryt I.25 = Pryt I.15 = Pryt I.04 = Pryt I.23 = Pryt I.12 = Pryt I.01 = Pryt I.19 = Pryt I.08 = Pryt I.27 = Pryt I.16 3 July 3 July 4 July 3 July 3 July 3 July 4 July 3 July 3 July 3 July 365 366 365 365 365 366 365 365 365 366 O I O O O I O O O I = II Skir 6 = Skir 16 = Skir 28 = II Skir 9 = Skir 19 = Hek 01 = Skir 13 = Skir 24 = II Skir 5 = Skir 15 H (-) H (-) F (+) F (+) H (-) [H (-)] F (+) F (+) F (+) H (-) 384 355 354 384 354 354 384 354 384 355 = Pryt I.05 = Pryt I.24 = Pryt I.14 = Pryt I.03 = Pryt I.21 = Pryt I.10 = Pryt X.34 = Pryt I.18 = Pryt I.06 = Pryt I.25 4 July 3 July 3 July 3 July 4 July 3 July 3 July 3 July 4 July 3 July 365 365 365 366 365 365 365 366 365 365 O O O I O O O I O O = Skir 26 = II Skir 7 = Skir 18 = Skir 29 = Skir 11 = Skir 22 = Hek 03 = Skir 14 = Skir 25 = II Skir 6 H (-) H (-) F (+) F (+) F (+) F (+) [F (+)] F (+) H (-) H (-) Civil Intercalation: V I S IA A I W W I V S After VerEqu After SumSol After AutEqu After WinSol Before SumSol Before AutEqu Before WinSol Before VerEqu Theory: Theory: Theory: Theory: 2nd 2nd 2nd 2nd Elaph, Moun, Thar, or Skir Hek, Met, or Boid Boid, Pyan, Maim, or Pos Pos, Gam, Anth, or Elaph Actual: Actual: Actual: Actual: Thar, Skir Boid Pos Elaph Tables here supercede Tables 9-10 & 15 in AYP (pp. 177-178, 180). I now consider those obsolete. k For the years 426/5-423/2 BCE, moreover, see Chap. XX, pp. xxx-xxx = The Logistai Inscription. The years 420/19 & 419/8 BCE are addressed Chap. XX (pp. xxx-xxx) = Antiphon VI. The analysis of IG I3 377 (= IG I2 304B = Tod 92 = Fornara 158) presented in the Primer (pp. 207-214) stands = The Choiseul Marble. Additionally, this seventy year schema shows what ought have unfolded if ancient Athenians had continuously, rigidly, and accurately followed astronomical reckonings for both the Archontic and Boulitic Calendars. In other words, these Calendar Equations present the oft needed but ever elusive baseline or calibration “template.” k) More specifically, the Tables given in the Primer (mevn) offer an attempted summation (or synthesis) of ancient Athenian calendrical studies as they then existed. The present Tables (dev) reflect my contribution to those debates. I have no doubt both Profs. Meritt & Pritchett would have vigorously objected to (parts of) my proposals. CHRISTOPHER PLANEAUX ATTIC INTERCALATIONS Table X: 432/1 to 403/2 BCE Julian Year Civil Intercalation Hek. 1 Number of Days 432/1 431/0 430/29 429/8 428/7 427/6 426/5 425/4 424/3 423/2 O IS O O WI V O O S I A O V I S 17 July 07 July 25 July 13 July 03 July 22 July 11 July 29 June 18 July 08 July 355 383 354 355 384 354 354 384 355 384 O O 27 July 15 July 04 July 23 July 12 July 01 July 20 July 09 July 28 July 17 July 06 July 25 July 14 July 02 July 21 July 11 July 30 June 18 July 08 July 27 July 422/1 421/0 420/19 419/8 418/7 417/6 416/5 415/4 414/3 413/2 412/1 411/0 410/09 409/8 408/7 407/6 406/5 405/4 404/3 403/2 V WI V O O S I A O V I S O O V IS O O W I V O O S I A O V I S O (Option 1) Calendar Equation Pryt. I.1 Number of Days Conciliar Intercalation Calendar Equation Full / Hollow = Pryt I.15 = Pryt I.05 = Pryt I.22 = Pryt I.11 = Pryt I.01 = Pryt I.20 = Pryt I.08 = Pryt X.32 = Pryt I.16 = Pryt I.06 3 July 3 July 4 July 3 July 3 July 3 July 4 July 3 July 3 July 3 July 365 366 365 365 365 366 365 365 365 371 O I O O O I O O O [I] = Skir 16 = Skir 27 = II Skir 9 = Skir 20 = Hek 01 = Skir 12 = Skir 24 = Hek 05 = Skir 15 = Skir 25 H (-) F (+) H (-) H (-) [F (+)] F (+) F (+) [H (-)] H (-) H (-) 354 354 384 354 355 384 354 384 355 354 = Pryt I.19 = Pryt I.08 = Pryt X.32 = Pryt I.15 = Pryt I.04 = Pryt X.29 = Pryt I.12 = Pryt I.01 = Pryt I.20 = Pryt I.10 9 July 8 July 9 July 9 July 9 July 8 July 9 July 9 July 9 July 8 July 365 366 365 365 365 366 365 365 365 366 O I O O O I O O O I = II Skir 13 = Skir 23 = Hek 06 = Skir 17 = Skir 27 = Hek 08 = Skir 20 = Hek 01 = II Skir 11 = Skir 22 F (+) H (-) [H (-)] F (+) H (-) [F (+)] F (+) [H (-)] H (-) F (+) 384 354 354 384 355 354 384 355 384 354 = Pryt X.34 = Pryt I.17 = Pryt I.06 = Pryt X.30 = Pryt I.13 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 9 July 9 July 9 July 8 July 9 July 11 Jul 30 Jun 18 Jul 08 Jul 27 Jul 365 365 365 366 367 354 384 355 384 354 O O O I [I] O I O I O = Hek 04 = II Skir 15 = Skir 26 = Hek 07 = Skir 18 = Hek 01 = Hek 01 = Hek 01 = Hek 01 = Hek 01 [F (+)] F (+) F (+) [H (-)] H (-) [F (+)] [H (-)] [H (-)] [F (+)] [F (+)] Calendar Equation Pryt. I.1 Number of Days Conciliar Intercal. Calendar Equation Full / Hollow = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 = Pryt I.01 16 July 4 July 22 July 12 July 2 July 20 July 9 July 29 June 17 July 5 July 354 383 355 355 384 354 355 383 354 384 O I O O I O O I O I Table X: 402/1 to 393/2 BCE Julian Year Civil Intercal. Hek. 1 Number of Days 402/1 401/0 400/399 399/8 398/7 397/6 396/5 395/4 394/3 393/2 O IS O O S I A O O S I A O V I S 16 July 04 July 22 July 12 July 02 July 20 July 09 July 29 June 17 July 05 July 354 383 355 355 384 354 355 383 354 384 V = Hek 01 = Hek 01 = Hek 01 = Hek 01 = Hek 01 = Hek 01 = Hek 01 = Hek 01 = Hek 01 = Hek 01 [F (+)] [H (+)] [H (-)] [F (+)] [F (+)] [F (+)] [H (-)] [F (+)] [H (-)] [H (-)] Civil Intercalation: V I S IA A I W W I V S After VerEqu After SumSol After AutEqu After WinSol Before SumSol Before AutEqu Before WinSol Before VerEqu Theory: Theory: Theory: Theory: 2nd 2nd 2nd 2nd Elaph, Moun, Thar, or Skir Hek, Met, or Boid Boid, Pyan, Maim, or Pos Pos, Gam, Anth, or Elaph Actual: Actual: Actual: Actual: Thar, Skir Boid Pos Elaph CHRISTOPHER PLANEAUX ENDNOTES inside 384 Days: 461/0, 458/7, 455/4, 453/2, 444/3, 442/1, [434/3], 425/4, [423/2], [419/8], 409/8, 406/5, and 393/2 BCE; finally, 354 inside 383 Days: 395/4 BCE. 10 Pleiavde~: the ancient identification for what marked a “rising” and “setting” of this asterism within the constellation Taurus, or simply a constellation itself, becomes a bit more complicated than perhaps appreciated. Nine stars, which by naked eye indeed appear as seven, span more than a degree (or four minutes) across the sky: Atlas (27 Tau), Pleione (28 Tau), Alkyone (h Tau), Merope (23 Tau), Maia (20 Tau), Elektra (17 Tau), Celaeno (16 Tau), Asterope (21 Tau), and Taygeta (q Tau). Galilea Galilei, for instance, identified thirty-six stars within the cluster, e.g. Asterope is actually two stars (Sterope I & II); Alkyone = brightest (mag. 2.85). Consequently, what the “typical ancient Greek farmer” living during the Classical Age (if such a creature ever existed) would have considered as the “Pleiades”appearing and disappearing upon the horizon grows frustratingly obtuse, i.e., whether just some or most or all or only the brightest star(s) must first appear or disappear when the Sun rises or sets to mark the specific day. AYP 245-248, 279. 11 Third reason: HR h Tau (Alkyone) thus the Pleiades occurred in Attike approx. 4:47 on 29/30 Apr @ LHA 17h20m or Az. +73°04′ (ca. 461 bce). This puts the cluster just north of due east from Lykabettos Hill. More importantly, Helios resided about 5° to the north just entering Civil Twilight at the time. Spotting Alkyone, unlike Arktouros, would take some effort and skill thus the first appreance not proving obvious or clear. 12 The rest of the chapter synthesizes material from D. MacDowell, Athenian Homicide Law in the Age of the Orators (Manchester 1963); The Law of Classical Athens, Aspects of Greek and Roman Life, ed. H. Scullard (Ithaca 1978) 113-122; M. Gagarin, Drakon and Early Athenian Homicide Law (New Haven 1981); R. Parker, Miasma: Pollution and Purification in Early Greek Religion (Oxford 1983); A. Boegehold, The Lawcourts at Athens: Sites, Buildings, Equipment, Procedure and Testimonia, Athenian Agora XXVIII (Princeton 1995); A Harrison, The Law of Athens: Volume II2 (London 1998) 36-43; I. Arnaoutoglou, Ancient Greek Laws: A Sourcebook (New York 1998) 71-73. 13 This statement possesses caveats for risings and settings. The precise angle of lunar orbit to the visible horizon changes with the latitude of the observer. Latitude also affects the times that the Moon becomes visible over the horizon as well as when it vanishes along the same Longitude. Elevation of the observer will also affect the precise time the Moon becomes visible or disappears. AYP 97-130. 14 Phratries (fratrivai) in general and the Apatouria in particular, with regard to ancient Athenian politeiva, remains a rather involved and quite complex debate. The inference here nonetheless becomes the ritual festival’s signifigance diminished. Parker, ARH 270; S. Lambert, The Phratries of Attica, Michigan Monographs in Classical Antiquity (Ann Arbor 1993) 143-189. 15 D. Feeney, Caesar’s Calendar: Ancient Time and the Beginnings of History (Berkeley 2007); J. Rüpke, The Roman Calendar from Numa to Constantine: Time, History and the Fasti (Wiley 2011). 16 See RE s.v. “Kalendar;” E. Bickerman, Chronology of the Ancient World, Aspects of Greek and Roman Life, H. Scullard, ed. (Ithaca 1974) 20-21 with bibliography. Christopher Planeaux